arXiv subjects

Michael Roy

Publications and source records attributed to Michael Roy.

3 recordsLinked to original sources

arXiv2025

A Structure-Preserving Assessment of VBPBB for Time Series Imputation Under Periodic Trends, Noise, and Missingness Mechanisms

Incomplete time-series data compromise statistical inference, particularly when the underlying process exhibits periodic structure (e.g., annual or monthly cycles). Conventional imputation procedures rarely account for such temporal dependence, leading to attenuation of seasonal signals and biased estimates. This study proposes and evaluates a structure-preserving multiple imputation framework that augments imputation models with frequency-specific covariates derived via the Variable Bandpass Periodic Block Bootstrap (VBPBB). In controlled simulations, we generate series with annual and monthly components, impose Gaussian noise across low, moderate, and high signal-to-noise regimes, and introduce Missing Completely at Random (MCAR) patterns from 5% to 70% missingness. Dominant periodic components are extracted with VBPBB, resampled to stabilize uncertainty, and incorporated as covariates in Amelia II. Compared with baseline methods that do not model temporal structure, the VBPBB-enhanced approach consistently yields lower imputation error and superior retention of periodic features, with the largest gains observed under high noise and when multiple components are included. These findings demonstrate that explicitly modeling periodic content during imputation improves reconstruction accuracy and preserves time-series structure in the presence of substantial missingness.

stat.AP↗

arXiv2025

Enhancing Data Completeness in Time Series: Imputation Strategies for Missing Data Using Significant Periodically Correlated Components

Missing data is a pervasive issue in statistical analyses, affecting the reliability and validity of research across diverse scientific disciplines. Failure to adequately address missing data can lead to biased estimates and consequently flawed conclusions. In this study, we present a novel imputation method that leverages significant annual components identified through the Variable Bandpass Periodic Block Bootstrap (VBPBB) technique to improve the accuracy and integrity of imputed datasets. Our approach enhances the completeness of datasets by systematically incorporating periodic components into the imputation process, thereby preserving key statistical properties, including mean and variance. We conduct a comparative analysis of various imputation techniques, demonstrating that our VBPBB-enhanced approach consistently outperforms traditional methods in maintaining the statistical structure of the original dataset. The results of our study underscore the robustness and reliability of VBPBB-enhanced imputation, highlighting its potential for broader application in real-world datasets, particularly in fields such as healthcare, where data quality is critical. These findings provide a robust framework for improving the accuracy of imputed datasets, offering substantial implications for advancing research methodologies across scientific and analytical contexts. Our method not only impute missing data but also ensures that the imputed values align with underlying temporal patterns, thereby facilitating more accurate and reliable conclusions.

stat.ME↗

arXiv2010

Levels in the toposes of simplicial sets and cubical sets

The essential subtoposes of a fixed topos form a complete lattice, which gives rise to the notion of a level in a topos. In the familiar example of simplicial sets, levels coincide with dimensions and give rise to the usual notions of n-skeletal and n-coskeletal simplicial sets. In addition to the obvious ordering, the levels provide a stricter means of comparing the complexity of objects, which is determined by the answer to the following question posed by Bill Lawvere: when does n-skeletal imply k-coskeletal? This paper answers this question for several toposes of interest to homotopy theory and higher category theory: simplicial sets, cubical sets, and reflexive globular sets. For the latter, n-skeletal implies (n+1)-coskeletal but for the other two examples the situation is considerably more complicated: n-skeletal implies (2n-1)-coskeletal for simplicial sets and 2n-coskeletal for cubical sets, but nothing stronger. In a discussion of further applications, we prove that n-skeletal cyclic sets are necessarily (2n+1)-coskeletal.

math.CT↗